Which of the following features of genetic codes allow bacteria to produce human insulin by recombinant $\text{DNA}$ technology?

The set of solutions of the equation $(\sqrt{3}-1) \sin \theta+(\sqrt{3}+1) \cos \theta=2$ is

$A$ rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V$. Assuming the radius of the earth to be $R$ and negligible air resistance,the maximum height attained by the rocket above the surface of the earth is

Manganese is required in

Observe the following reaction: $2 A + B \longrightarrow C$. The rate of formation of $C$ is $2.2 \times 10^{-3} \ mol \ L^{-1} \ min^{-1}$. What is the value of $-\frac{d[A]}{dt}$ (in $mol \ L^{-1} \ min^{-1}$)?

The solution of $\tan y \frac{dy}{dx} = \sin(x+y) + \sin(x-y)$ is